Geodesic
On orthogonally additive injections and surjections
Commentationes Mathematicae, Tome 55 (2015) no. 2, p. 157−162.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Let \(E\) be a real inner product space of dimension at least 2 and \(V\) a linear topological Hausdorff space. If \(\operatorname{card}E\leq \operatorname{card} V\), then the set of all orthogonally additive injections mapping \(E\) into \(V\) is dense in the space of all orthogonally additive functions from \(E\) into \(V\) with the Tychonoff topology. If \(\operatorname{card}V\leq \operatorname{card}E\), then the set of all orthogonally additive surjections mapping \(E\) into \(V\) is dense in the space of all orthogonally additive functions from \(E\) into \(V\) with the Tychonoff topology.
DOI : 10.14708/cm.v55i2.1109
Classification : 39B55, 46C99, 46A99
Mots-clés : orthogonal additivity, inner product space, linear topological space, Tychonoff topology, dense set 
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Karol Baron. On orthogonally additive injections and surjections. Commentationes Mathematicae, Tome 55 (2015) no. 2, p.  157−162. doi : 10.14708/cm.v55i2.1109. http://geodesic.mathdoc.fr/articles/10.14708/cm.v55i2.1109/

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